I agree with your determinant. Can you post the rest of your working?
m+2n+p=5
3m+4n+p=8
m-6n+2p=4
There are 2 ways taught us to solve for this using matrix.
The Inverse method and Row-Echelon method.
In row echelon method i got this answer:
m=1
n=1/2
p=3
i know the answer is correct because when i substitute it to the equations above, i get the correct answer.
(1)+2(1/2)+(3)=5
3(1)+4(1/2)+(3)=8
1-6(1/2)+2(3)=4
My problem is, when I use the Inverse method, i get the determinant -18, and the rest of the process gives me a wrong answer.